1. Field of the Invention
The present invention relates to an optical device for scanning light via a mirror, and more specifically relates to a resonant optical device for optical scanning at high speed by resonating a member supporting a mirror.
2. Description of the Related Art
Conventionally, optical scanning is accomplished by using a galvanometer to rotate a mirror. Since the galvanometer is mechanically driven by a motor and is provided with a reflective surface that characteristically scans light in a wide range, the overall construction including the drive mechanism is large and requires a large amount of energy to produce the drive force, thereby making it difficult to scan a wide range at high speed.
A resonant optical device has been developed which rotates a mirror at high speed using the resonance phenomenon. An example of a known resonant optical device is shown in FIG. 19. This resonant optical device comprises a rod-like iron resonator 51, reflecting mirror 52 mounted on the leading end of the resonator 51, stationary platform 53 to which the base end of resonator 51 is fixedly mounted, oscillators 54 formed of the same material as resonator 51 and protruding horizontally therefrom, permanent magnets 55a and 55b located above and below the ends of oscillators 54, and coils 56a and 56b through which the oscillators 54 pass. Magnets 55a and 55b, and coils 56a and 56b, are fixedly attached to platform 53.
The iron oscillators 54 are magnetized by a current supplied to coils 56a and 56b, and the current flow direction and wire winding direction of coils 56a and 56b are set so as to have mutually reverse polarities at opposite ends of oscillators 54. Magnets 55a and 55b have the polarities shown in the drawing, such that bilateral ends of the magnetized oscillators 54 receive a force in mutually opposite vertical directions. Therefore, oscillators 54 oscillate via an alternating current flowing through coils 56a and 56b so as to rotate rod-like resonator 51 around its axis.
Resonator 51 resonates with the oscillation of oscillators 54 so as to induce the oscillation of mirror 52 mounted on the tip of resonator 51, by matching the frequency of the alternating current oscillating the oscillators 54 to the natural frequency of the resonator 51. Since the base end of the resonator 51 is fixedly attached to platform 53, the oscillation amplitude (oscillation angle) of resonator 51 is greatest at the leading end, such that mirror 52 also oscillates with the same amplitude. Optical scanning is accomplished by changing the direction of reflection of incident light via the oscillation of mirror 52.
A transverse cross section of resonator 51 is shown in FIG. 20. Resonator 51 is formed so as to be thick at the base and tapered gradually toward the tip. A through hole 51a is formed near the base end, and a channel 51b is formed near the tip. Oscillator 54 is fixedly attached through the hole 51a, and reflecting mirror 52 is fixedly mounted in channel 51b so as to be gripped from both opposite sides.
The aforesaid resonant optical device is capable of optical scanning at high speed compared to a mechanically driven galvanometer, and can be constructed more compactly, thereby broadening its range of applications. For example, various proposals have recently been made for head-mounted displays (HMD) of the scanning type wherein light is directed to the retina and an image is projected by optical scanning on the retina, and resonant optical devices are suitable for the scanning units of such display devices due to their capability of high speed optical scanning and compactness. Resonant optical devices are desirable due to their greater breadth of scanning range and higher scanning speed.
In the case of a torsion spring of uniform thickness and having a mirror mounted on the tip and a fixed base, if the natural frequency is designated fn, the spring constant is designated k, moment of inertia of the mirror is designated I, and the moment of inertia of the spring itself is ignored, the natural frequency fn can be expressed by equation (1) below. EQU fn=1/(2.multidot..pi.).multidot.(k/I).sup.1/2 =1/(2.multidot..pi.).multidot.{(.pi..multidot.G.multidot.d.sup.4)/(32.mult idot.I.multidot.L)}.sup.1/2 (1)
where the value G represents horizontal elasticity, d represents the diameter of the spring, and L represents the length of the spring. Equation (1) shows that the natural frequency is proportional to the square of the spring diameter d, and inversely proportional to the square root of the spring length L. Increasing the spring diameter d and shortening the spring length L is effective in achieving high speed oscillation, i.e., increasing the natural frequency fn of the spring.
On the other hand, the spring amplitude limit .theta.lim can be expressed by equation (2) below when the torsion stress tolerance is designated .tau.. EQU .theta.lim=2.multidot.L.multidot..tau./(G.multidot.d) (2)
Equation (2) shows the amplitude limit .theta.lim is proportional to the spring length L, and inversely proportional to the spring diameter d. Therefore, lengthening the spring length L and reducing the spring diameter d is effective in increasing the spring amplitude limit .theta.lim.
As can be seen, the conditions which must be satisfied to increase the natural frequency fn and the conditions which must be satisfied to increase the amplitude limit .theta.lim are mutually contradictory, relative to the size of the spring. Under this limitation, the conventional resonator shown in FIG. 20 is shaped so as to be gradually tapered from the base toward the tip to increase the natural frequency fn as well as increase the amplitude limit .theta.lim. However, there is a natural limitation to increasing the natural frequency fn and amplitude limit .theta.lim simply by the shape and size of the spring.
When considering the moment of inertia of the torsion spring itself, the natural frequency fn is expressed by equation (3) below. EQU tan {2.multidot..pi..multidot.fn.multidot.L/(G/.rho.).sup.1/2 }=d.sup.4 .multidot.(.rho..multidot.G).sup.1/2 /(64.multidot.I.multidot.fn) (3)
where .rho. represents the density of the spring. Equation (3) not only expresses factors stipulating spring diameter d, spring length L, and modulus of transverse elasticity G, but also density .rho., and natural frequency fn.